Q28 / 50 · Manipal (MET) 2024 · Mathematics

Total number of even divisions of 2079000 which are divisible by 15 are

A
54
B
128
Correct answer
C
108
D
72

Solution

$\because 2079000=2^3 \times 3^3 \times 5^3 \times 7 \times 11$ for the divisor to be even and divisible by $15 ; 2,3$ and 5 must be occur once. There, the total number of required divisors are $3 \times 3 \times 3 \times 2 \times 2=108$

Hence, the correct answer is option: 'C'.

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